In order to improve the appearance of the light exit surfaces—formed from converting elements—of light-emitting diodes, light-emitting diode arrangements and other products based on light-emitting diodes, attempts are made to impart a more highly color-neutral appearance to the converting element by means of a material layer placed in front. The material layer at least partly shields the converting element from the externally incident light from the standpoint of the observer. By way of example, an outer enveloping bulb or some other capping layer or coating is applied, which can also have scattering properties. Scattering can be achieved, for example, by the roughening of the surface of such a capping layer, by incorporated scattering particles or air bubbles or by a capping layer which, for example, is translucent but not completely transparent. The scattering has the effect that when the light-emitting diode is switched off, the inherent color of the phosphor and of the converting element admixed therewith is not visible or is visible only with attenuation. In return, it is conventionally also accepted that the same properties of the capping layer lead to disadvantages during the operation of the light-emitting diode. In particular, it is accepted that the scattering of the capping layer of the converting element leads to light losses when the light-emitting diode emits light. At the present time there is no prospect of a satisfactory solution.